GRADING AND SCREENING 253
have already been given represent a compromise between good screen work and capacity.
Beyond the point where the particle clings to the screen under the forces which cause it to rise on the screen on the first part of its path, it rises further by momentum but it decreasingly partakes of the motion of the screen. When the particle reaches the highest point of its path it falls along an ellipse whose major axis is that of an ellipse formed by a vertical plane passed through the inner cylindrical surface of the trommel. The minor axis of this ellipse is of course equal to the internal diameter of the screen. The particle does not, however, return to a position at the bottom of the screen, but as Louis has shown, to a point above this; that is the particle will fall through an arc which is double that through which it rises from the point where it ceases to partake entirely of the up motion of the screen. On the next cycle of the up and down motion the particle will rise and partake of the entire motion of the screen through an arc which is equal to the arc through which it will rise by momentum.
The mathematical discussion of the motion of a particle in a trommel as given by Louis very well explains the characteristic swinging of a bank in a trommel. No attempt is made by him to measure the effect of centrifugal force. In the theory as stated by Richards the particle is assumed to rise to a point where its sliding angle is reached, modified by the effect of centrifugal force. This theory does not explain the swinging of the bank but it yields figures showing at what rate of rotation the particles will be carried entirely around the screen.
Rotation of the Bank.—In order to understand this the mind must be fixed on the particles in the bank collectively, remembering that each is endeavoring to pass through the cycles of motion which have already been described. The lower lines of particles in contact with the screen endeavor to push the upper ones above the point where they would be carried if alone in the screen; and it is quite evident that the moment they reach a point which is in the plane at which the size and kind of material in the trommel will slide on itself, they will slide down the face of the bank and when they reach the lower edge they will again pass up to their former position unless in the meantime eliminated by passage through the screen apertures. This action causes a rotation of the bank which is greatest at the borders and diminishes inwardly towards its center. The upper bounding surface of the bank is a more or less unstable plane. Except by pressure of the bank above or by accidental position immediately over an opening the possibility of a particle passing through the apertures is nil while the bank is rising and partaking of the motion of the screen. While the bank is ascending still further under momentum since there is relative motion between the screen and bank there is some opportunity to effect screening but as must be evident the best part of a saw-tooth path to effect screening is when the bank is sliding down. The particles which slide down the upper face of the bank come momentarily in contact with unoccupied screen surface where they may be eliminated.
The effect of the rotation of the bank is to bring the coarse particles to its periphery. As the coarse particles which appear at the upper edge under rotation will tend to roll farther and faster down the upper unstable surface of the bank and report at the lower edge and by progressive increase of this action as the material works down through the screen there is a tendency to the accumulation of the coarse particles at the bank's periphery. While the interstitial or shaking down effect is very much less in a trommel than on a shaking screen this action does exist so that the end result of the bank rotation is to bring coarse particles into contact with the screen with the interstices filled in with fine particles. It is this action which permits of